"Divisible by 3": Other approach? How do I use the probability formula?

Link

https://gre.magoosh.com/questions/859

Question

FAQ: What's the other approach? How do I use probability alone?

Answer

The basic probability formula is, as we saw in the first method, ^{(# of desired outcomes)} / _{(# of possible outcomes)}. We can use that to find the probability of getting a desired number with each draw from the list.

We know we are looking specifically to get a 3, 6, 9, 12, or 15 each time, so there are 5 possible numbers which would give us that "success." Altogether, there are 7 numbers in the list, so the chance of getting a number that's divisible by three is ⁵/₇.

The chance of getting a "success" on the second draw is ⁴/₆, because we have one less number in the list (no replacement).

Similarly, the chance on the third draw is ³/₅. If we want to find the probability of two or more events coming to pass, we want to multiply the probabilities together. That's ⁵/₇ * ⁴/₆ * ³/₅ = ⁶⁰/₂₁₀ = ²/₇

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